Question

A body when projected vertically up, covers a total distance D during its time of flight. If there were no gravity, the distance covered by it during the same time is equal to

• A. 0
• B. D
• C. 2D
• D. 4D

Answer 1

Answer: (C)

2D

Answer 2

The displacement of the body during the time t as it reaches the point of projection

⇒ S = 0 ⇒ v₀t − $\frac{1}{2}$ gt² = 0

⇒ $t\ = \ \frac{\text{2}\text{v}_{0}}{g}$

During the same time t, the body moves in absence of gravity through a distance

D′ = v.t, because in absence of gravity g = 0

⇒ D′ = $v_{0}\text{ }\left( \frac{\text{2}\text{v}_{0}}{g} \right)\text{ } = \text{ }\frac{\text{2}\text{v}_{0}^{2}}{g}$ …(1)

In presence of gravity the total distance covered is

= D = 2H = $2\ \frac{v_{\text{02}}^{2}}{\text{2g}}\ = \ \frac{v_{0}^{2}}{g}$ …(2)

(1) ÷ (2) ⇒ D′ = 2D, Hence (3) is correct.